Abstract

A laser confocal radius measurement (LCRM) method is proposed for high-accuracy measurement of the radius of curvature (ROC). The LCRM uses the peak points of confocal response curves to identify the cat eye and confocal positions precisely. It then accurately measures the distance between these two positions to determine the ROC. The LCRM also uses conic fitting, which significantly enhances measurement accuracy by restraining the influences of environmental disturbance and system noise on the measurement results. The experimental results indicate that LCRM has a relative expanded uncertainty of less than 10 ppm for both convex and concave spheres. Thus, LCRM is a feasible method for ROC measurements with high accuracy and concise structures.

© 2014 Optical Society of America

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References

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  1. A. J. Leistner and W. J. Giardini, “Fabrication and sphericity measurements of single-crystal silicon spheres,” Metrologia 31, 231–243 (1994).
    [CrossRef]
  2. K. Yoshizumi, T. Murao, J. Masui, R. Imanaka, and Y. Okino, “Ultrahigh accuracy 3-D profilometer,” Appl. Opt. 26, 1647–1653 (1987).
    [CrossRef]
  3. W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
    [CrossRef]
  4. Z. Malacara, “Angle, prisms, curvature, and focal length measurements,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), Chap. 17, pp. 808–825.
  5. Y. Xiang, “Focus retrocollimated interferometry for long-radius-of-curvature measurement,” Appl. Opt. 40, 6210–6214 (2001).
    [CrossRef]
  6. L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1967 (1992).
    [CrossRef]
  7. U. Griesmann, J. Soons, and Q. Wanga, “Measuring form and radius of spheres with interferometry,” CIRP Ann. 53, 451–454 (2004).
    [CrossRef]
  8. H. Ye and L. Yang, “Accuracy and analysis of long-radius measurement with long trace profiler,” Chin. Opt. Lett. 9, 102301 (2011).
    [CrossRef]
  9. Q. Hao, Q. Zhu, and Y. Hu, “Random phase-shifting interferometry without accurately controlling or calibrating the phase shifts,” Opt. Lett. 34, 1288–1290 (2009).
    [CrossRef]
  10. T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
    [CrossRef]
  11. W. Zhao, R. Sun, L. Qiu, and D. Sha, “Laser differential confocal radius measurement,” Opt. Express 18, 2345–2360 (2010).
    [CrossRef]
  12. R. Sun, L. Qiu, J. Yang, and W. Zhao, “Laser differential confocal radius measurement system,” Appl. Opt. 51, 6275–6281 (2012).
    [CrossRef]
  13. W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12, 5013–5021 (2004).
    [CrossRef]
  14. T. Wilson, “Confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, 1990), Chap. 1, pp. 1–64.
  15. M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999).

2013 (1)

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

2012 (1)

2011 (1)

2010 (1)

2009 (1)

2004 (2)

U. Griesmann, J. Soons, and Q. Wanga, “Measuring form and radius of spheres with interferometry,” CIRP Ann. 53, 451–454 (2004).
[CrossRef]

W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12, 5013–5021 (2004).
[CrossRef]

2001 (2)

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

Y. Xiang, “Focus retrocollimated interferometry for long-radius-of-curvature measurement,” Appl. Opt. 40, 6210–6214 (2001).
[CrossRef]

1994 (1)

A. J. Leistner and W. J. Giardini, “Fabrication and sphericity measurements of single-crystal silicon spheres,” Metrologia 31, 231–243 (1994).
[CrossRef]

1992 (1)

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1967 (1992).
[CrossRef]

1987 (1)

Born, M.

M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999).

Davies, A. D.

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

Evans, C. J.

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

Gao, D.

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

Giardini, W. J.

A. J. Leistner and W. J. Giardini, “Fabrication and sphericity measurements of single-crystal silicon spheres,” Metrologia 31, 231–243 (1994).
[CrossRef]

Griesmann, U.

U. Griesmann, J. Soons, and Q. Wanga, “Measuring form and radius of spheres with interferometry,” CIRP Ann. 53, 451–454 (2004).
[CrossRef]

Guo, J.

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

Hao, Q.

Hu, Y.

Imanaka, R.

Leistner, A. J.

A. J. Leistner and W. J. Giardini, “Fabrication and sphericity measurements of single-crystal silicon spheres,” Metrologia 31, 231–243 (1994).
[CrossRef]

Malacara, Z.

Z. Malacara, “Angle, prisms, curvature, and focal length measurements,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), Chap. 17, pp. 808–825.

Masui, J.

Meng, J.

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

Murao, T.

Okino, Y.

Qiu, L.

Schmitz, T. L.

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

Selberg, L. A.

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1967 (1992).
[CrossRef]

Sha, D.

Soons, J.

U. Griesmann, J. Soons, and Q. Wanga, “Measuring form and radius of spheres with interferometry,” CIRP Ann. 53, 451–454 (2004).
[CrossRef]

Sun, R.

Tan, J.

Wang, Y.

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

Wanga, Q.

U. Griesmann, J. Soons, and Q. Wanga, “Measuring form and radius of spheres with interferometry,” CIRP Ann. 53, 451–454 (2004).
[CrossRef]

Wilson, T.

T. Wilson, “Confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, 1990), Chap. 1, pp. 1–64.

Wolf, E.

M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999).

Xiang, Y.

Yang, J.

Yang, L.

Ye, H.

Yoshizumi, K.

Zhao, W.

Zhu, Q.

Appl. Opt. (3)

Chin. Opt. Lett. (1)

CIRP Ann. (1)

U. Griesmann, J. Soons, and Q. Wanga, “Measuring form and radius of spheres with interferometry,” CIRP Ann. 53, 451–454 (2004).
[CrossRef]

Metrologia (1)

A. J. Leistner and W. J. Giardini, “Fabrication and sphericity measurements of single-crystal silicon spheres,” Metrologia 31, 231–243 (1994).
[CrossRef]

Opt. Commun. (1)

W. Zhao, J. Guo, L. Qiu, Y. Wang, J. Meng, and D. Gao, “Low transmittance ICF capsule geometric parameters measurement using laser differential confocal technique,” Opt. Commun. 292, 62–67 (2013).
[CrossRef]

Opt. Eng. (1)

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31, 1961–1967 (1992).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Proc. SPIE (1)

T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature,” Proc. SPIE 4451, 432–447 (2001).
[CrossRef]

Other (3)

Z. Malacara, “Angle, prisms, curvature, and focal length measurements,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 2007), Chap. 17, pp. 808–825.

T. Wilson, “Confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, 1990), Chap. 1, pp. 1–64.

M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999).

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Figures (11)

Fig. 1.
Fig. 1.

LCRM principle, where PBS is the polarized beam splitter, P is the quarter wave plate, Lc is the collimating lens, Lobj is the objective, and MO and CCD are the microscope objective and detector of the VPH, respectively.

Fig. 2.
Fig. 2.

Effect of figure error Φ(ρ,θ) on the ROC.

Fig. 3.
Fig. 3.

Confocal response curves affected by figure error Φ(ρ,θ): (a) affected by primary spherical aberration A040ρ4 and (b) affected by primary astigmatism A022ρ2cos2θ.

Fig. 4.
Fig. 4.

Light path schematic with VPH deviating from the Lc focus.

Fig. 5.
Fig. 5.

Angles between the LCRM axes.

Fig. 6.
Fig. 6.

Experimental setup.

Fig. 7.
Fig. 7.

Test spheres used in the experiments.

Fig. 8.
Fig. 8.

Single measurement result of the test convex sphere.

Fig. 9.
Fig. 9.

Multiple measurement results of the convex sphere.

Fig. 10.
Fig. 10.

Single measurement result of the test concave sphere.

Fig. 11.
Fig. 11.

Multiple measurement results of the concave sphere.

Tables (1)

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Table 1. Δra and Δmr with Different Aberrations

Equations (20)

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IA(u)=|02π01Pc(ρ,θ)Pc(ρ,π+θ)Po(ρ,θ)Po(ρ,π+θ)exp(iuρ2)ρdρdθ|2,
IA(u)=[sin(u/2)u/2]2.
IB(u)=|02π01exp[i2kΦ(ρ,π+θ)]exp(iuρ2)ρdρdθ|2.
IB(u)=[sin(u/2)u/2]2.
Φ(ρ,θ)A040ρ4+A022ρ2cos2θ+A031ρ3cosθ+A120ρ2+A111ρcosθ+,
Δar=k(ravgrref)2πλ(2A040+A022),
IBA040(u)=|02π01exp(i2kA040ρ4)exp(iuρ2)ρdρdθ|2,
IBA022(u)=|02π01exp[i2kA022ρ2cos2(π+θ)]exp(iuρ2)ρdρdθ|2.
rmearavg=1k(ΔmrΔra)=0.
IA(u,uδM)={sin(u/2uδM/4)u/2uδM/4}2,
IB(u,uδM)={sin(u/2uδM/4)u/2uδM/4}2,
uδM=π2λδMD2fc2.
ΔuA=ΔuB=uδM2.
Δaxial=r(1cosα·cosβ),
u1=Δaxial3=13r(1cosβ·cosγ).
u=u12+u22.
u=u12+u22=0.0022+0.052=0.05μm.
δ=URconvex×100%=0.112.688961×1000×100%7.8ppm.
u=u12+u22=0.0022+0.062=0.06μm.
δ=URconcave×100%=0.1212.725021×1000×100%9.4ppm.

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